Fractional generalizations of Rodrigues-type formulas for Laguerre functions in function spaces

Generalized Laguerre polynomials, L(a) n, verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them. © 2021 by the authors. Licensee MDPI, Basel, Switzerland